CHEM 1125Q Mini-Exam 3: Solutions

Solutions

homogeneous mixtures of two or more substances

Solvent + Solute (s) = ?

solution

Aqueous solution

Solution with H2O as solvent

Concentrations

Describe the quantity of solute dissolved in a specific quantity of either solvent or total solution.

Solutions will form when the solute and solvent have dissimilar polarities t/f

false, similar polarities

Most gaseous and solid solutes will dissolve only to a certain extent in a given liquid at a given temperature t/f

true

Solubility

the maximum amount of solute that dissolves in a specific amount of solvent

Solubility is usually expressed as...

grams of solute in 100 grams of solvent, usually water

g of solute / 100 g water

unsaturated solution

can dissolve more solute

saturated solution

Contains the maximum amount of solute

supersaturated solution

Contains more than the maximum solute, which then forms a precipitate

When a solution forms, the solute particles become surrounded by solvent particles in a process called ________

solvation

Hydration

solution process with water as the solvent

For a solution to form solute-solvent attractions ≥

solute-solute + solvent-solvent attractions

Enthalpy of solution (ΔHºsolution):

ΔHºsolution = ΔHºsolute + ΔHºsolvant + ΔHºsolvation hydration

enthalpy changes (ΔH) involved when ionic compounds dissolve in water

ΔH(solution) ​= [ΔH(ionic bonds)​ + ΔH(H₂O-H₂O​)] + ΔH(ion-dipole​)

Label these processes as endo- or exothermic:

1. Solute-solute interactions broken →

2. Solvent-solvent interactions broken →

3. Solute-solvent (ion-dipole) interactions form →

1. Endo

2. Endo

3. Exo

Negative ΔHsolution

Solute-solvent intermolecular interactions are stronger than the solute-solute and solvent intermolecular interactions

Positive ΔHsolution

Stronger solute-solute interactions. Strong london dispersion forces. less soluble in water.

Alcohols of four or more C atoms are positive or negative ΔHsolution?

positive

Which solution, [G] or [H], is at a lower temperature?

(G has more molecular motions, while H has less molecular motion)

A. [G]

B. [G] and [H] are at the same temperature.

C. [H]

D. The temperature of the solutions cannot be determined from the images

C

Which three factors affect solubility?

1. Structure

2. Pressure

3. Temperature

What is structure in terms of solubility?

Strength and number of interactions among solute particles AND interactions of solvent molecules determine solubility

Immiscible

Liquid solutes and solvents that are not soluble in each other (polar + non-polar)

An increase in temperature favors exothermic process t/f

false, favors endothermic process

At low to moderate pressure, the concentration of a gas increases with the pressure t/f

true

Henry's Law

The concentration of a sparingly soluble gas is proportional to the partial pressure of the gas

What is the formula for Henry's Law

C(gas) = k(H) P(gas)

P(gas) is the partial pressure of the gas over the solution

C(gas) is the concentration of the gas

k is a constant (the Henry's Law constant)

How are carbonated beverages made?

Pressure of carbon dioxide is kept high by pressurizing the container

The concentration of oxygen in blood is proportional to the partial pressure of oxygen in the air we inhale (proportional to the atmospheric pressure) t/f

true

Increased pressure while diving increases gas solubility in bodily fluids

➢ Rising too rapidly to the surface can lead to bubbling of gas forming in the blood and other fluids in the body; this phenomenon is called the _____

bends

Lake Titicaca is located high in the Andes Mountains between Peru and Bolivia. Its surface is 3811 m (12 507 ft) above sea level, where the average atmospheric pressure is 0.636 atm. During the summer, the average temperature of the water's surface rarely exceeds 15°C. What is the solubility of oxygen in Lake Titicaca at that temperature? Express your answer in molarity and mg/L. (Dry air is 20% O2)

K at 15°C is 1.5 x 10^-3

= 6.1056 mg/L

C(O2) = K(H)P(O2)

Patm = 0.636 atm

T = 15 °C

P(O2) = X(O2) P(T)

? = 1.50 x 10^-3 mol/L atm x P(O2)

X(O2): 0.2 x 0.636 = 0.1272 atm

C(O2) = 1.50 x 10^-3 mol/L atm x 0.1272

= 1.908 x 10^-4 mol/L

Concentration of O2 in mg/L

1.908 x 10^-4 x 32 g x 1000 mg = 6.1056 mg/L

The concentration of a solution is expressed as:

Amount of solute/amount of solution

amount of solute/amount of solvent

small component/large component

dilute

low concentration of solute

concentrated

high concentration of solute

Units of concentration: Molarity (M)

M = moles solute/liters of solution

Units of concentration: Mole fraction (X)

X = moles solute/total moles

Units of concentration: Molality (m)

m = moles solute/kilograms of solvent

Units of concentration: Mass percentage (%m)

%m = mass of component/mass of solution x 100%

Mass percentage is also referred as:

1. Percent mass, ___

2. Percent weight, ____

3. Weight/weight percent, ____

4. Parts per million ____

5. Parts per billion ____

1. %m

2. %W

3. w/w%

4. ppm

5. ppb

volume percentage

the concentration of a solution formed by dissolving a liquid solute in a liquid solvent.

%vol

v/v%

Volume percentage formula

volume solute/volume solution x 100%

Copper sulfate is widely used as a dietary supplement for animal feed. A lab technician prepares a "stock" solution of CuSO4 by adding 79.80 g of CuSO4 (MM=159.6 g/mol) to enough water to make 500.0 mL of solution. An experiment requires a 0.1000M solution of CuSO4.

a) What is the molarity of the CuSO4 "stock" solution.

b) How would you prepare 1.500 L of 0.1000 M from the stock solution?

a) CuSO4: 79.8 g, 159.6 g/mol

final volume: 500 mL x 1L/1000mL = 0.5 L

n(CuSO4): 79.8 g x 1/159.6 g = 0.5 mol CuSO4

M = 0.5 moles/0.5 L = 1.00 M

b) Dilution: [CuSO4] = 1 M, V = ?

Working solution = CuSO4 = 0.1 M, V = 1.5 L

(1) V1 = (0.1) (1.5) = 0.15 L

Take 0.15 L of the stock and add enough water to make 1.50 L

A 5.0g sample of spinal fluid contains 3.75mg of glucose. What is the percent by mass of glucose in spinal fluid?

% mass = mass solute/mass of solution x 100

solute: glucose

solution: spinal fluid

3.75 mg x 1g/1000mg = 3.75 x 10^-3 g

% glucose = 3.75 x 10^-3/5.0 g x 100 = 0.075%

Hydrogen peroxide is used by some water treatment systems to remove the disagreeable odor of sulfides in drinking water. It is available commercially in a 20.0% by mass aqueous solution. What is the mole fraction of H2O2 (MM=34.02 g/mol)?

H2O2 -- 20% by mass of solution --> 100g of solution, 20 g of H2O2, 80g H2O

Solute: H2O2

Solvent: H2O

X = n(H2O2)/n(total)

n(H2O2): 20g H2O2 x 1 mol/34.02 g = 0.588 mol

n(H2O): 80g H2O x 1 mol/18.02 g = 4.44 mol

n(total): 0.588 mol + 4.44 mol = 5.03

Xn: 0.588 mol/5.03 mol = 0.117

What is the molarity of ions in a 0.0773 M solution of (NH4)2SO4?

A. 0.0783 M

B. 0.155 M

C. 0.232 M

D. 0.0773 M

C

Glucose, C6H12O6,in water is often used for intravenous feeding. Sometimes sodium ions are added to the solution. A pharmacist prepares a solution by adding 2.0 mg of sodium ions (in the form of NaCl), 6.00 g of glucose, and 112 g of water. What is the molality of the glucose in solution?

2.0 mg Na+ 6.00 g glucose -------- 112g water H2O

m = moles solute/kg solvent

1. n glucose: 6 g glucose x 1/180.16 g = 0.0333 mol glucose

2. kg solvent: 112 g x 1kg/1000g = 0.112 kg

m = 0.033/0.112 = 0.297 m

A solution of urea CO(NH2)2 (MM = 60.1g/mol) has a solute mass percent of 55.0%,

(a) convert the concentration unit to molality

(b) find the mole fraction of solvent

a) Molality: m = nsolute/kg solvent

1. urea solution: solute = urea, solvent = H2O

55% mass: n 100g solution: 55 g urea, 45 g H2O

2. n solute (urea): 55 g urea x 1 mol/60.1 g = 0.91514 mol urea

3. kg solvent (H2O): 45 g x 1 kg/1000 g = 0.045 kg H2O

m = 0.91514 mol/0.045 kg = 20.336 mol/kg = 20.24 m

b) X solvent = n solvent/n total

1. solute: 55% urea, solvent of H2O

55 g of urea, 45g of H2O

2. n urea: 55 g urea x 1 mol/60.1 g = 0.91514 mol

3. n H2O: 45g H2O x 1 mol/18.02 g = 2.497 mol

4. n total: 0.91514 + 2.497 = 3.412365

5. X solvent: 2.497 mol H2O/3.1412365 mol = 0.73175

X (H2O) = 0.732

What happens to the number of moles of C12H22O11 (sucrose) when a 0.20 M solution is diluted to a final concentration of 0.10 M?

A. The number of moles of C12H22O11 decreases.

B. The number of moles of C12H22O11 increases.

C. The number of moles of C12H22O11 does not change.

D. There is insufficient information to answer the question.

C

Colligative properties of a solution depend only on the....

number of solute particles and not on the chemical identity of the solute

Osmotic Pressure (π)

A colligative property, pressure required to stop osmosis

Vapor Pressure Lowering, Boiling Point Elevation, and Freezing Point Lowering are examples of _________ properties

colligative

What does it mean that colligative properties follow limiting laws, and at what concentration do these laws stop accurately applying?

because their ideal behavior is approached only as the solution becomes more dilute. These laws are accurate up to about 1 M concentration; above this, deviations occur due to increased solute-solute interactions.

Substances that dissolve in water can undergo an either physical or chemical change that yields ions t/f

true

Colligative properties depend on...

the concentration of dissolved particles

What happens when a strong or weak electrolyte dissolves in water?

When a strong or weak electrolyte dissolves in water, it dissociates into ions. Each formula unit of the compound separates into multiple charged particles (cations and anions).

This is why electrolytes yield more than one mole of particles per mole of solute—they break apart into ions rather than staying as whole molecules.

For electrolytes, how does the particle concentration compare to solute concentration?

The particle concentration (M) is greater than the solute's molar concentration.

van 't Hoff factor (𝑖)

The ratio of the concentrations of solute particles in a solution to the concentration of particles that would be there if a solute did not dissociate

Semipermeable membrane

Channels through which solvent (water) flows

What is osmosis?

The spontaneous movement of a solvent (usually water) through a semipermeable membrane.

In which direction does water move during osmosis?

From a region of high water concentration (low solute) to low water concentration (high solute).

What happens to the level of the solution with higher solute concentration during osmosis?

It rises.

What happens to the concentrations of the two solutions over time during osmosis?

They become equal.

Hypotonic solution

a solution that causes a cell to swell because of osmosis

Isotonic solutions

solutions separated by a membrane and containing an equal concentration of non-permeating solutes

Hypertonic solutions

solutions that cause cells to shrink or shrivel due to loss of water

What happens with if osmotic pressure is greater than π applied?

Water flows in the opposite direction — this is reverse osmosis.

What is the formula for osmotic pressure?

π = iMRT

If the total concentration of solute particles in the fluid inside a red blood cell is 0.310 M, what is the osmotic pressure of this fluid at body temperature (37°C)? The membrane surrounding the cell is semipermeable.

[particles] = 0.310 M

i = 1

T = 310 K

π = iMRT

π = 1 (0.31) (0.08026) (310) = 7.71 atm

A 47 mg sample of water-soluble non-electrolyte is isolated from a South African tree. The sample is dissolved in enough water to make 2.50 mL of solution. The osmotic pressure of the solution is 0.489 atm at 25°C. What is the molar mass of the compound?

47 mg

i = 1

π = 0.489 atm

T = 298 K

Vgol = 2.50 mL

1. M = π/iRT = 0.489 / 1 x 0.08206 x 298 = 0.0199968 mol/L

2. n solute: 0.0199968 mol/L x 0.0025 L = 4.9992 x 10^-5 mol

3. MM: 0.047 g/4.9992 x 10^5 = 940 g/mol

If solutions [A] and [I] were separated by a semipermeable membrane, as shown in [E], what molecules or ions would flow across the membrane and in what direction?

[A] = higher concentration of solute

[I] = lower concentration of solute

A. Water molecules would flow toward [A].

B. There would be no flow across the membrane.

C. The ions represented by the orange and green spheres would flow toward [I].

D. Water molecules would flow toward [I].

E. The ions represented by the orange and green spheres would flow toward [A].

A

Vapor pressure

the pressure exerted by a gas in equilibrium with its liquid phase at a given temperature

Volatile

having a significant vapor pressure at a given temperature. The higher the vapor pressure, the more volatile

Raoult's Law

The total vapor pressure of an ideal solution depends on the vapor pressure of each component in the solution and its mole fraction in the liquid mixture

Raoult's Law formula

P (total) = x1P1 + x2P2 + x3P3 + ...

What are ideal solutions?

Solutions where intermolecular interactions between molecules have comparable strengths.

What is the vapor pressure of a solution prepared by dissolving 13 g of heptane (C7H16) in 87 g of octane (C8H18) at 25ºC? The vapor pressure of heptane and octane at 25ºC are 31 torr and 11 torr, respectively?

Heptane: 13 g --> 31 Torrs, 100.20 g/mol

Octane: 87 g --> 11 Torrs, 114.23 g/mol

P(solution) = X(hep)P(hep) + X(oct)P(oct)

ni: Heptane: 13 g x 1/100.20 g = 0.1297 mol heptane

Octane: 87 g x 1/114.23 g = 0.7616 mol octane

n(total) = 0.1297 + 0.7616 = 0.89132

Xi: heptane, n(heptane)/n(total) = 0.1297/0.89132 = 0.1455

Octane, n(octane)/n(total) = 0.7616/0.89132 = 0.8545

P(total) = 0.1455 x 31 + 0.8545 x 11 = 13.9086 Torr

What is a nonvolatile solute?

A substance whose vapor pressure is negligible (Pº ≈ 0).

How does a nonvolatile solute affect a volatile solvent like water?

It lowers the vapor pressure of the solvent.

What happens to the vapor pressure of a volatile solvent when a nonvolatile solute is added?

The vapor pressure is lowered.

How does the amount of nonvolatile solute affect vapor pressure?

The more solute particles, the lower the vapor pressure.

Does the chemical identity of the solute affect the vapor pressure lowering?

No, it depends only on the number of solute particles, not their identity.

Most of the world's supply of maple syrup is produced in Quebec, Canada, where the sap from maple trees is evaporated until the concentration of sugar (mostly sucrose) in the sap reaches 66% by weight. What is the vapor pressure in atm of a 66% aqueous solution of sucrose (MM=342.30 g/mol) at 100ºC?

sucrose nonvolatile

MM = 342.30 g/mol

T = 100 ºC

66%

H2O solvent

T = 100ºC

P(H2O) = 1 atm

P(solute) = X solv P solv

i. X(solv): n(H2O)/n(total)

ii. n(H2O): 34g x 1/18.02 = 1.8858 mol H2O

n(suc): 66g x 1/342.3 g = 0.1928 mol H2O

n(total) = 1.8868 + 0.1928

66% --> 100 g solution: 66g sucrose + 34 g H2O

X = 1.8868/(1.8868 + 0.1928) = X = 0.9072

iii. P(solute) = 0.9072 x 1 = 0.91 atm

When london forces increase, solubility decreases t/f

true

The density of an aqueous solution containing 25% of ethanol (C2H5OH) by mass is 0.950 g/mL.

a) Calculate the molality of this solution

b) Calculate its molarity

c) What volume of the solution would contain 0.275 mole of ethanol

a) 7.235 mol/kg

b) 5.155 mol/L

c) 0.0534 L

An aqueous solution is both 0.2 m and 0.227 M. The solute has a molar mass of 115 g/mol. Calculate the density of the solution and the mass percent of the solute in solution.

1.16 g/mL and 2.24%

Boiling point elevation

The decrease in the vapor pressure of the solution relative to that of pure solvent at all temperatures corresponds to an increase in the boiling point of a solution

Freezing point depression

Solutions freeze at lower temperatures than their pure solvents

Boiling point elevation is a ____________ property

colligative

Boiling point elevation is a colligative property meaning...

it does not depend on identity of solute and does depend on the concentration of the solute in molality

Boiling Point Elevation Formula

ΔTb ​= Kb​×m

ΔTb = increase in boiling point (°C)

Kb = boiling point elevation constant (°C·kg/mol)

m = molality of the solute (mol/kg solvent)

What happens to the boiling point of a solvent when a nonvolatile solute is dissolved in it, and why?

The boiling point increases because the nonvolatile solute lowers the solvent's vapor pressure, so the solution must be heated to a higher temperature for its vapor pressure to equal the external pressure.

Freezing point depression is a ___________ property

colligative

Freezing point depression is a colligative property, meaning...

it does not depend on identity of solute and depends on the concentration of the solute in molality.

Freezing Point Depression Formula

∆𝑇𝑓 = 𝚤𝑘𝑓𝑚

ΔTf = decrease in freezing point (°C)

Kf = freezing point depression constant (°C·kg/mol)

m = molality of the solute (mol/kg solvent)

What happens to the freezing point of a solvent when a nonvolatile solute is dissolved in it, and why?

The freezing point decreases because the solute lowers the solvent's vapor pressure, making it harder for the liquid to solidify.

What is the boiling point of seawater in which the concentration of sea salts is equivalent to 0.560 mol NaCl/kg seawater, the density of seawater is 1.025 g/mL, and the van't Hoff factor of NaCl is 1.85?

1 kg seawater (solution) : 967 g H2O (solvent) + 0.56 mol NaCl (solute)

iNaCl: exp = 1.85, theor = 2

kb = 0.52

1. m: 0.560 mol /0.967 kg = 0.579 m

2. ∆Tb = ikbm

∆Tb = 1.85 x 0.52 x 0.579 = 0.5571 = 0.56 °C

3. 100 °C H2O

100.56 °C seawater

Which solution has the lowest freezing point?

A. 0.10 m KCl

B. 0.15 m glucose

C. 0.15 m MgCl2

D. 0.30 m sucrose

E. More information is needed

C

Note: Colligative property, freezing point depression, 0.15 M MgCl2 (0.45 M) is going to have the largest depression

KCl → K⁺ + Cl⁻ → i≈2

Glucose → non-electrolyte → i=1

MgCl₂ → Mg²⁺ + 2Cl⁻ → i≈3

Sucrose → non-electrolyte → i=1

Which of these 0.1 M aqueous solutions will have the LOWEST vapor pressure?

A. Na2SO4

B. C6H12O6

C. MgSO4

D. KCl

E. Solutions with the same concentration always have the same vapor pressure

A

What is the N2 concentration in a diver's blood at a depth where the total pressure is 2.5 atm? Air is 78% N2 by volume. The Henry's Law constant for nitrogen in blood serum is about 8 x 10^-7 mol L^-1 mmHg ^-1

Cgas = kPgas

Pgas: Pi = XiPtotal

XH2: P = (0.78)(2.5) = 1.95 atm

1.95 atm x 760 mmHg = 1492 mmHg

Cgas = (8 x 10^-7)(1492) = 1.185 X 10^-3 mol/L